Speaker
Description
This work investigates cochlear amplification in a transmission line model whose local elements are critical oscillators operating near a Hopf bifurcation. Here, starting from a physically based micromechanical description of the cochlea, the governing equations are reformulated into normal form, allowing the parameters of the reduced model to be directly related to measurable physical quantities. A transmission-line cochlear model including two-dimensional fluid coupling is solved in time domain with the state space technique and pressure Green’s functions. The analysis further demonstrates the rapid growth of the cochlear response as the system approaches the Hopf instability. The distance from the bifurcation is expressed in terms of physiologically meaningful parameters, such as the strength of the active force and the cutoff frequency associated with the outer hair cell transmembrane potential. The proposed formulation therefore establishes a direct connection between abstract nonlinear oscillator theory and the physical processes governing cochlear mechanics. Preliminary results show how approaching the critical regime it is possible to get large gain dynamics in the peak region. Interestingly, although the nonlinear force is coupled to the relative mode only, both modes show the same nonlinear behavior, due to the back-action on the pressure associated with the focusing phenomenon.